Let the width of the rectangular room is w feet. And length is 6 feet longer than twice the width , that is length is
[tex](2w+6) feet[/tex]
And the given perimeter is 216 feet.
Perimeter is the sum of all sides. That is
[tex]w + 2w+6+w +2w+6 = 216[/tex]
Combining like terms
[tex]6w +12 =216
\\
6w = 204
\\
w = 34 feet[/tex]
So the width is 34 feet and length is 6 more than twice of 34, therefore length is
[tex](2*34+6)feet = 74 feet[/tex]
